City's season will now kick off on Saturday, August 11 after their Capital One Cup tie was moved forward.
The first-round visit to League One Notts County was scheduled to take place the following Tuesday.
But Barnsley agreed to cancel their planned friendly at Valley Parade, allowing City and County to change their cup date.
A Saturday afternoon clash should guarantee a bigger crowd with more away fans likely to make the trip.
It also gives City a clear week before they open their League Two campaign at Gillingham the Saturday after.